# Transfer Function for a negative feedback loop

Discussion in 'Math' started by smarch, Nov 20, 2010.

1. ### smarch Thread Starter Active Member

Mar 14, 2009
52
0
Hi guys would appreciate the help.
I am having trouble with this question.

From the JPEG I have a attached:

Determine the equivalent T.F. G(s) in form of G(s) = $\frac{p}{qs+r}$, where p, q, r are constants.

I have tried working it out, but got into a mess. Help please, how do you do it?

Thanks

• ###### TF.jpg
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Last edited: Nov 20, 2010
2. ### guitarguy12387 Active Member

Apr 10, 2008
359
12

In general, for a closed loop system, you have:

TF = (direct path gain)/(1 - sum of loop gain)

From there it is just algebra to get into the right form

3. ### smarch Thread Starter Active Member

Mar 14, 2009
52
0
I come to :

C(s) = R(s).(10/3s - 5) - C(s)(40/3s - 20)

Am I on the right track?
I have limited notes on this and have tried to follow it as they are in the notes, but it is quite a different problem to that one.

4. ### guitarguy12387 Active Member

Apr 10, 2008
359
12
Yeah that looks about right i think.

Now just solve for C(s)/R(s)

5. ### smarch Thread Starter Active Member

Mar 14, 2009
52
0
How do you complete it all the way through to get G(s) = $\frac{p}{qs+r}$

6. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
First read here:http://en.wikipedia.org/wiki/Control_theory in the section Closed Loop Tranfer Funtion. In your case you have C=5, P=$\frac{2}{3s}-1$ and F=-4;

Try to calculate the Transfer Function H(s).

Post it and we will discuss more.

7. ### krishna chaitanya New Member

Nov 8, 2010
5
0
TF = (direct path gain)/(1 - sum of loop gain)..

it will give ans for this...